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National Committee of Ukraine by Theoretical and Applied Mechanics Taras Shevchenko National University of Kyiv

Institute of Mechanics of NAS of Ukraine Institute of Mathematics of NAS of Ukraine Institute of Cybernetics of NAS of Ukraine

XVIII International Conference

DYNAMICAL SYSTEM MODELLING

AND STABILITY INVESTIGATION

MODELLING

&

STABILITY

ABSTRACTS OF CONFERENCE REPORTS

Kiev, Ukraine

May 24-26, 2017

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ВІСНИК

Київського національного університету імені Тараса Шевченка

The various aspects of theoretical and applied researches are represented in abstracts of conference reports.

Problems of adequate mathematical model of studied processes are considered.

Problems of control synthesis and stability investigation of movements are separately allocated. Significant

numbers of papers are devoted to modeling of economic problems, biological and social phenomena. Big

quantity of reports presented at the conference is devoted to the problems of applied mechanics.Logic-

mathematical methods of modeling are considered.

Prepared by A.V.Shatyrko

Recommended for printing by Scientific Council

of Computer Science and Cybernetics faculty

of Taras Shevcheno National University of Kyiv.

Scientific Editor: Dr.Sc., Prof.

Khusainov D.Ya.

Reviewer: Dr.Sc., Prof.

Boychuk A.A.

В тезисах докладов конференции представлены различные аспекты теоретических и прикладных

исследований. Рассмотрены вопросы создания математических моделей, адекватно описывающих

исследуемые объекты.

Отдельно рассмотрены проблемы синтеза управления и исследования устойчивости движения.

Значительное количество работ связано с моделированием экономических, биологических и

социальных процессов. Большое количество работ посвящено проблемам теоретической и

прикладной механики. Рассмотрены логико-математические методы моделирования.

Подготовлено А.В.Шатырко

Рекомендовано к печати Ученым Советом

факультета компьютерных наук и кибернетики

Киевского национального университета

имени Тараса Шевченко

Научный редактор: доктор физ.-мат. наук, профессор

Хусаинов Д.Я.

Рецензент: доктор физ.-мат. наук, профессор

Бойчук А.А.

В тезах доповідей конференції представлено різні аспекти теоретичних та прикладних досліджень.

Розглянуто питання створення математичних моделей, що адекватно описують об‟єкти.

Окремо розглянуто проблему синтезу керування та дослідження стійкості руху. Значна кількість

праць пов‟язана із моделюванням економічних, біологічних та соціальних процесів. Велика кількість

праць присвячена проблемам теоретичної та прикладної механіки. Розглянуті логіко-математичні

методи моделювання.

Підготовлено А.В.Шатирко

Рекомендовано до друку Вченою Радою

факультету комп‟ютерних наук та кібернетики

Київського національного університету

імені ТарасаШевченка

Вчений редактор: доктор фіз.-мат. наук, профессор

Хусаінов Д.Я.

Рецензент: доктор фіз.-мат. наук, профессор

Бойчук А.А.

УДК

ББК

D

ISBN

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During the period May 24-26, 2017 the traditional International Conference “Dynamical Systems Modeling

and Stability Investigation” was held. The members of committees were

SCIENTIFIC COMMITTEE

Aliev F. (Baku, Azerbaidzhan),

Andreev A.S. (Ulyanovsk, Rusia),

Amirgalieva S. (Almaty, Kazakhstan),

Babaev A.E. (Kyiv, Ukraine),

Bastinec J. (Brno, Czech Republic),

Boychuk A.A. (Kyiv, Ukraine),

Cherevko I.V. (Chernitsi, Ukraine),

Chikrii A.O. (Kyiv, Ukraine),

Diblik J. (Brno, Czech Republic),

Dimitrov G. (Sofia, Bulgaria),

Demidenko G.V. (Novosibirsk, Russia),

Domoshnitsky A. (Ariel, Israel),

Ivanov A.F. (Penn State, U.S.A.),

Kalitin B.S. (Minsk, Belorussia),

Karandzhulov L.I. (Sofia, Bulgaria),

Kolomodaev M. (Almaty, Kazakhstan),

Kubenko V.D. (Kyiv, Ukraine),

Krack Yu.V. (Kyiv, Ukraine),

Makarov V.L. (Kyiv, Ukraine),

Martinyuk A.A. (Kyiv, Ukraine),

Ruzickova M. (Zilina, Slovak Republic),

Sadyrbaev F. (Riga, Latvia)

Shmeidel E. (Byalystok, Poland),

Vasiliev S.N. (Moscow, Russia)

ORGANIZING COMMITTEE

Babaev A.A. (Kyiv, Ukraine),

Bychkov O. (Kyiv, Ukraine),

Chernii D.I (Kyiv, Ukraine),

DzhalladovaI.A.(Kyiv,Ukraine,Vice Chairman)

Grygorenko A.Ya. (Kyiv, Ukraine),

Kapustyan O.I. (Kyiv, Ukraine),

Kashpur O.F. (Kyiv, Ukraine),

Khusainov D.Ya. (Kyiv, Ukraine, Chairman),

Liashenko O. I. (Kyiv, Ukraine),

Limarchenko O.S. (Kyiv, Ukraine)

Mazko A.P. (Kyiv, Ukraine),

Nikitchenko N.S. (Kyiv, Ukraine),

Onyshchenko S.M. (Kyiv, Ukraine),

Podchasov N.P. (Kyiv, Ukraine),

Shatyrko A.V (Kyiv, Ukraine, Vice Chairman),

Shkilniak S.S. (Kyiv, Ukraine),

Zhuk Ya. A. (Kyiv, Ukraine).

The Conference covers the following topics:

1. Mathematical methods of system investigation.

Investigation of differential, functional-differential and difference systems.

Investigation of system stability, controllability and optimization.

Bifurcations and chaos in dynamical systems.

Lyapunov's methods in system investigation.

2. Methods and technologies of computer modeling.

Numerical Methods of Mathematical Physics.

Method and Technology computer calculations.

Specialized software and systems.

Software and Systems Modeling

3. Modeling and investigation of processes in mechanics.

Mathematical modeling in composite materials of mechanics.

Modeling and investigation of dynamical processes in elastic and hydroelastic systems.

Mathematical modeling in connected fields of mechanics.

4. Method of control and complex systems research

Methods of control and optimization.

The continuous-discrete systems

Methods of differential games.

Fuzzy modeling and systems with uncertainty.

Modelling in economy and ecology.

5. Logic-mathematical methods of modeling.

Methods and tools of subject domains specifications.

Methods and tools of software systems description.

Modal and temporal formalisms of systems modeling

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Також в цей же період відбулася

КОНФЕРЕНЦІЯ-СУПУТНИК

ВСЕУКРАЇНСЬКА НАУКОВО-ПРАКТИЧНА КОНФЕРЕНЦІ МОЛОДИХ ВЧЕНИХ

«Теоретичнi та прикладнi аспекти

застосування iнформацiйних технологiй в галузi природничих наук»

ПРОГРАМНИЙ КОМІТЕТ

Голова комітету

Дімітров Георгі заступник декана Faculty of

Information Sciences, професор, ULSIT

(Софія, Болгарія),

Заступник голови

Мішель Пезеріл, президент університету

міста Ле Ман (Ле Ман, Франція),

Заступник голови

Бичков Олексій, завідувач кафедри

Програмних систем і технологій, к.ф.-м.наук,

доцент (Київ, Україна),

Шевченко Віктор – професор кафедри

Програмних систем і технологій, д.т.н,

професор (Київ, Україна),

Турбал Юрій – директор навчально-

наукового інституту заочно-дистанційного

навчання, д.т.н. (Рівне, Україна)

ОРГАНІЗАЦІЙНИЙ КОМІТЕТ

Іванов Є.В. – асистент кафедри Програмних

систем і технологій, к.ф.-м. наук,

Поляков С.А. – доцент кафедри Програмних

систем і технологій, к.ф.-м. наук, доцент

Поперешняк С.В. – доцент кафедри Програмних

систем і технологій, к.т. наук, доцент

Супрун О.М. – доцент кафедри Програмних

систем і технологій, к.ф.-м. наук, доцент

Коваленко Л.Б. – декан факультету

комп‟ютерних наук ОДЕКУ, к.г.н., доцент

Кузніченко С.Д. – доцент кафедри

інформаційних технологій, к.г.н.

Терещенко Т.М. – доцент кафедри

інформаційних технологій, к.т.н.

Шуптар Н.Й. - асистент кафедри інформаційних

технологій, голова Наукового товариства

студентів, аспірантів, докторантів та молодих

вчених ОДЕКУ

Великодний С.С. – доцент кафедри

інформаційних технологій, к.т.н., голова

Наукового товариства факультету комп‟ютерних

наук ОДЕКУ

Секції конференції:

Математичні основи інформаційних технологій

Геоінформаційні системи та технології

Інформаційні технології в системах моніторингу навколишнього середовища

Технології вбудованих і мобільних систем

Batyuk Liliya Vasilyevna, Ph.D. (Biology), Associate professor of Department of Medical and Biological

Physics and Medical Information Science

Kharkiv National Medical University, Kharkiv, Ukraine

e-mail: liliya-batyuk@ukr.netAstapovich Dmitry Fedorovich, engineer of Department of Molecular and Medical biophysics

V. N. Karazin Kharkiv National University, Kharkiv, Ukraine

e-mail: astapovich.2012@mail.ru

Berest Vladimir Petrovich, Ph.D. (Phys.–Math.), Associate professor of Department of Molecular and

Medical biophysics, Head of Department of Molecular and Medical biophysics

V. N. Karazin Kharkiv National University, Kharkiv, Ukraine

e-mail: vpberest@hotmail.com

Kizilova Natalia Nikolaevna, Dr. Sci. (Phys.–Math.), Prof. of Department of Theoretical and Applied

Mechanics, Head of Department of Theoretical and Applied Mechanics

V. N. Karazin Kharkiv National University, Kharkiv, Ukraine

e-mail: n.kizilova@gmail.com

MATHEMATICAL MODELLING OF CONFORMATIONAL DYNAMICS OF DNA

BY DIELECTRIC SPECTROSCOPY

Batyuk L.V., Astapovich D.F., Berest V.P., Kizilova N.N.,

Between the different forms of DNA, with changing external conditions, conformational

transitions occur. Conformational transitions have both cooperative and noncooperative nature.

Cooperative conformational transitions are associated with the need to overcome the energy barrier.

Besides, there is a boundary of conformations, for example, “A-B junction”, which, without

breaking the stacking, leads to the bending of the double helix of DNA, which is important for the

processes of DNA supercoiling and its interaction with proteins [1]. One of the factors determining

the conformation of DNA is its hydrated environment. The water molecules sorbed on the surface

of the biopolymer form a multilayered hydrated shell with a regular structure of hydrogen bonds

[2]. Such water bridges contribute significantly to the stabilization of DNA double helices, up to

70% in the enthalpy of B-DNA melting in moistened films and gels. The influence of the hydration

shell on the conformational state of DNA causes the researchers' interest in studying the properties

of water molecules in a hydrated shell. It is difficult to conduct such an analysis in solution,

because, for example, at usual DNA concentrations used in the study of UV spectra (10-6-10-5 g/ml),

the amount of water bound to DNA is 10-4-10-5 % of the total amount of water in the solution,

which leads to unrealistic requirements for the accuracy of measuring devices. Therefore, a

convenient model object for studying the properties of the hydrate shell is moistened DNA samples,

such as films and fibers. In addition, according to modern concepts in biological systems, there are

no free water molecules, so DNA in them, apparently, are not in solution, but, on the contrary,

compete for hydrated water with other substances.

In this paper we consider a model of bounded volume that describes the conformational

transitions of a DNA molecule induced by a change in the relative humidity of a sample. The

conformation of DNA is determined by its ion-hydrate environment. The DNA molecule is modeled

by a sequence of monomer units, of a certain length. The DNA molecules commonly used in the

experiment include 105 pairs of nucleotides, which allow us to use the methods of thermodynamics

in the description of DNA. The chain links can be in one of three conformational states: a

disordered form, and two conformations, between which reversible cooperative conformational

transitions are possible. Water molecules that are directly connected to the double helix of DNA

form an impermeable cationic primary hydrate shell, which includes 11-12 water molecules per

nucleotide. The water molecules associated with the primary hydrated shell due to hydrogen bonds

form a secondary hydrated DNA envelope. There are also tertiary, etc. hydrate shells, however, the

properties of the water molecules that form them, differ little from the properties of water molecules

far from DNA. The inclusion of DNA in the consideration of the hydrate environment requires the

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use of a device designed to describe open thermodynamic systems [3], using stochastic methods of

analysis, DNA exchanges water with the environment when the external conditions change.

Numerical modeling makes it possible to obtain a system of differential equations that describes

processes of sorption of water molecules and associated conformational transitions of nucleic acids.

The increase in relative humidity leads to an increase in the change in free energy during the

sorption of water moles due to the increase in the number of sorbed water molecules, which

changes the ratio of the minima and makes the conformational transition energetically favorable.

1. Retting M., Germann M.W., Wang S., Wilson W.D. Molecular basis for sequence-

dependent induced DNA bending / M. Retting // Chembiochem. – 2013. – P.323-331.

2. Badasyan A.V., Tonoyan Sh.A., Mamasakhlisov Y.Sh., Giacometti A., Benight A.S.,

Morozov V.F. Competition for hydrogen-bond formation in the helix-coil transition and protein

folding / A.V. Badasyan // Phys Rev E Stat Nonlin Soft Matter Phys. – 2011. – V. 83. – P. 1-9.

3. Heidari A. A Thermodynamic Study on Hydration and Dehydration of DNA and

RNA−Amphiphile Complexes / A. A. Heidari // J Bioeng Biomed Sci. - 2016. - P.1-2.

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